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-)A nonuniform, but spherically symmetric distribution of charge has a
charge density given as follows:
p(r) =
47tar?
for r <a
P(r) = 0 ,
for r 2 a
%3D
where a is the radius of the sphere and Q is the total charge of the sphere. a) prove
that the total charge within the sphere is indeed equal to Q (hint: for the spherical
symmetry, dV= 4rr dr); b) Using Gauss' law, derive expressions of the electric field at
distance r from the center in the cases of and r>a and r< a, respectively. (Use any
variable or symbol stated above along with the following as necessary: eo.)

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